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Firstly, constant amplitude P-Sa-Sm- Nc surface family is established. Secondly, four basic assumptions, i.e., monotonically increasing, non-coupling, separability and nonintersecting of fatigue damage accumulation are proposed from the viewpoint of both damage mechanics and fracture mechanics. Then the individual isodamage D-Sa-Sm-N surface under constant amplitude loading is constructed and the two-dimensional individual Miner’s rule is derived. Consequently, the two-dimensional probabilistic Miner’s rule (TPMiner) is established and proved for a population subjected to variable amplitude loading. Finally, with successfully experiment verification, TPMiner proves be to very useful and feasible in fatigue reliability theory.
Secondly, four basic assumptions, ie, monotonically increasing, non-coupling, separability and nonintersecting of fatigue damage accumulation are proposed from the viewpoint of both damage mechanics and fracture mechanics . The individual isodamage D-Sa-Sm-N surface under constant amplitude loading is constructed and the two-dimensional individual Miner’s rule is derived. The two-dimensional probabilistic Miner’s rule (TPMiner) is established and proved for a population subject Finally, with successfully experiment verification, TPMiner proves be to very useful and feasible in fatigue reliability theory.